osoitetaan

Osoitetaan is a Finnish verb form that comes from the verb osoittaa, meaning to show, indicate or demonstrate. In its present passive form, osoitetaan translates roughly as “it is shown” or “it is indicated.” It is commonly used in formal writing to state a result that will be or has been demonstrated, without naming who performs the demonstration.

In mathematical, logical, and scientific prose, the construction Osoitetaan, että … is a standard way to introduce a proposition to be proven. The subject is typically implicit, and the clause following että expresses the claim: “It is shown that …” The corresponding past tense is osoitettiin (“it was shown”), and the infinitive form is osoittaa.

Grammatical notes: osoitetaan is the present tense, passive voice of osoittaa. The form is characteristic of formal or technical text, and is less common in everyday speech, where authors may prefer active constructions such as näytetään or a different phrasing. Related forms include the infinitive osoittaa and the participle osoitettu (“shown”).

Examples:

- Osoitetaan, että kaikille n∈N pätee n^2 ≥ 0. (It is shown that for all natural numbers n, n^2 ≥ 0.)

- Osoitettiin, että ratkaisu on yksikäsitteinen. (It was shown that the solution is unique.)

Overall, osoitetaan functions as a formal, impersonal phrasing used to introduce proofs or demonstrated results in Finnish academic writing.

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